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A reduced model is introduced to represent an oscillation of a jet by edge tones. The edge tone is one of the indispensable elements in air-reed musical instruments, such as a recorder, a flute, a flue organ pipe, etc. The main approach is to obtain a representation by a one-dimensional partial differential equation (PDE) which is intended to shorten a computational time. Several parameter values are determined through a comparison between model functions and results by two-dimensional fluid mechanics calculations. Through a numerical integration of our model PDE and time measurements, it is shown that this model is applicable to real-time simulations to describe dynamics of air-reed instruments.

The aim of this paper is to shed new light on the tonal grammar of Icelandic and to complement the tone inventory as previously described in the literature (Árnason 1998). Specifically, types of pitch accents and edge tones and their combinations in neutral declaratives and questions, and in utterances containing narrow focus are addressed. Two pitch accent types (H* and L*) and two edge tones (H- and L-) are identified, for which evidence has not been found in previous research. Moreover, the paper shows for declaratives, that along with downstep, Icelandic has upstep across Intonational Phrases. Upstep applies to a series of pitch peaks. It may occur in neutral declaratives and in utterances with final narrow focus. Overall, the results of this study provide a substantial addition to our knowledge of Icelandic intonational phonology.

We study both, by experimental and numerical means the fluid dynamical phenomenon of edge tones. Of particular interest is the verification of scaling laws relating the frequency f to given quantities, namely d, the height of the jet, w, the standoff distance and the velocity of the jet. We conclude that the Strouhal number S d is related to the geometrical quantities through S d = C . (d/w) n with n 1, in contrast to some analytical treatments of the problem. The constant C of the experiment agrees within 13-15% with the result of the numerical treatment. Only a weak dependence on the Reynolds number with respect to d is observed. In general, a very good agreement of the experimental and the numerical simulations is found.

The unsteady global dynamics of a gravitational liquid sheet interacting with a onesided adjacent air enclosure, typically referred to as nappe oscillation, is addressed, under the assumptions of potential flow and absence of surface tension effects. To the purpose of shedding physical insights, the investigation examines both the dynamics and the energy aspects. An interesting re-formulation of the problem consists of recasting the nappe global behavior as a driven damped spring-mass oscillator, where the inertial effects are linked to the liquid sheet mass and the spring is represented by the equivalent stiffness of the air enclosure acting on the average displacement of the compliant nappe centerline. The investigation is carried out through a modal (i.e., time asymptotic) and a non-modal (i.e., short-time transient) linear approach, which are corroborated by direct numerical simulations of the governing equation. The modal analysis shows that the flow system is characterized by low-frequency and high-frequency oscillations, the former related to the crossing time of the perturbations over the whole domain and the latter related to the spring-mass oscillator. The low-frequency oscillations, observed in real life systems, are produced by the (linear) combination of multiple modes. The non-normality of the operator is responsible for short-time energy amplifications even in asymptotically stable configurations, which are confirmed by numerical simulations and justified by energy budget considerations. Strong analogies with the edge-tone problem are encountered; in particular, the integer-plus-one-quarter resonance criterion is uncovered, where the basic frequency to be multiplied by n + 1/4 is just the one related to the spacing among the imaginary parts of the eigenvalues.